⣿⣻⡟⣿⣽⣻⣟⣯⣟⣿⣻⣽⣻⣟⣯⣟⠿⣻⣽⡟⢿⣻⣟⡿⣽⣻⡟⣿⣽⣻⣟⣯⣟⣿⣻⣽ ⣯⢷⣻⢷⢯⡷⣞⣷⣻⣞⣷⣯⠷⠊⠁⠁⢀⣴⣦⡀⠀⠁⠈⠙⠳⣯⣟⡷⣯⢷⣞⣷⣻⣞⡷⣯ ⣟⣯⣟⣯⢿⣽⣻⣞⡷⣯⠟⠀⠀⠀⠀⣴⣾⣿⣿⠟⠀⠀⠀⠀⠀⠈⠻⣽⣯⣟⣾⣳⣟⡾⣽⣳ ⡿⣾⢽⣞⡿⣞⡷⣯⠿⠁⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⢀⣰⣦⡀⠀⠀⠀⠐⢿⣞⣷⣻⢾⣽⣳⣟ ⣿⣽⣻⢾⡽⣯⢿⡻⠁⠀⠀⠀⠺⣿⣿⣿⣧⡀⠀⣴⣾⣿⣿⣿⣦⡀⠀⠀⠈⣾⣳⢯⣟⣾⣳⢯ ⣷⣻⣞⣯⢿⡽⣯⡇⠀⣠⣄⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠋⠻⣿⣿⣦⡀⠀⢸⣯⣟⣾⣳⢯⡿ ⣏⣷⢿⡾⣏⡿⣷⠇⢾⣿⣿⣷⡀⠀⠀⢈⣿⣿⣿⣿⣇⠀⠀⠀⠈⢿⣿⣿⠇⢸⣷⢿⣾⣹⣏⡿ ⡿⣞⣯⢿⣽⣻⣽⡇⠀⠙⢿⣿⣿⣦⣶⣿⣿⣿⠿⣿⣿⣷⣄⠀⠀⠀⠙⠁⠀⢸⣞⡿⣞⡷⣯⣟ ⣿⡽⣞⡿⣞⡷⣯⢷⡀⠀⠀⠙⢿⣿⣿⡿⠟⠀⠀⠘⣿⣿⣿⣷⠄⠀⠀⠀⢠⡿⣯⢿⡽⣽⣳⢯ ⣷⣻⣽⣻⡽⣽⢯⣟⣷⡄⠀⠀⠀⠙⠛⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⢠⣾⢿⡽⣯⣟⡷⣯⢿ ⣯⢷⣯⢷⣻⣽⣻⣞⣷⣻⣆⡀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠁⠀⠀⠀⢀⣴⡿⣽⢯⣟⡷⣯⢿⡽⣯ ⣟⣿⣺⢯⡷⣯⢷⣻⣞⡷⣯⣟⣶⣄⡄⣀⠀⠙⠛⠁⠀⣀⢠⣤⣶⡿⣯⢿⣽⣻⢾⡽⣯⢿⣽⣳ ⣿⢾⡽⣯⢿⡽⣯⢷⡯⣟⣷⣻⢾⣽⣻⣽⣳⣟⣿⣳⣟⣯⢿⡽⣏⡿⣽⣻⢾⡽⣯⢿⣽⡻⣞⡷

⡷⣞⡻⣽⢿⣯⡽⢾⣻⣽⡿⣏⡽⢿⣯⣟⣳⣿⣟⣳⣽⣻⣽⢾⣻⣷⣟⡯⢷⣯⡽⢿⣯⡽⢾⣿ ⣳⣽⢿⣯⡽⢾⣻⣽⢿⣯⡿⣶⣤⢠⣀⠀⠁⠛⠙⠀⣀⡄⣄⣶⣟⣯⡷⣞⣻⢷⣯⡷⢯⣺⣿⣟ ⣯⡽⢿⣯⡷⣟⢯⣽⡿⣴⢀⠀⠀⠀⠁⠟⣿⣿⣿⢠⠀⠀⠀⠀⡀⣆⣻⣷⣞⣻⣽⣻⢷⣯⢷⣯ ⢿⣯⡷⣟⣯⡽⢿⣾⢠⠀⠀⠀⠁⠟⣿⣿⣿⣰⠀⠀⠀⠛⠙⠀⠀⠀⡄⣷⣟⢯⣽⡽⣻⣽⣻⣷ ⢯⣳⣽⡽⢿⣯⡿⢠⠀⠀⠀⠄⣷⣿⣿⣿⠘⠀⠀⠟⡿⣿⣿⢿⠙⠀⠀⡀⢷⣯⡷⣞⡿⣞⡽⣿ ⣟⣯⡷⣞⡿⣞⢸⠀⠁⠙⠀⠀⠀⣄⣷⣿⣿⠿⣿⣿⣿⣶⣦⣿⣿⢿⠙⠀⡇⣽⣻⣽⢿⣯⣞⡿ ⡿⣏⣹⣾⢿⣷⢸⠇⣿⣿⢿⠈⠀⠀⠀⣇⣿⣿⣿⣿⢈⠀⠀⡀⣷⣿⣿⢾⠇⣷⡿⣏⡾⢿⣷⣏ ⡿⢯⣳⣾⣟⣯⢸⠀⡀⣦⣿⣿⠻⠋⡟⣿⣿⣿⣿⣿⣿⠻⠈⠀⠀⣄⣠⠀⡇⣯⡽⢿⣯⣞⣻⣷ ⢯⣳⣾⣟⢯⣳⣾⠈⠀⠀⡀⣦⣿⣿⣿⣾⣴⠀⡀⣧⣿⣿⣿⠺⠀⠀⠀⠁⡻⢿⣯⡽⢾⣻⣽⣿ ⣟⣳⣽⢾⣻⣷⣞⢿⠐⠀⠀⠀⡀⣦⣰⢀⠀⠁⠟⣿⣿⣾⣠⠀⠀⠀⠁⠿⣯⡷⣞⡿⣞⢽⣾⡿ ⣳⣽⡾⣟⣳⣾⣟⣯⣽⠻⠈⠀⠀⠀⠀⠀⠟⣿⣿⣾⣴⠀⠀⠀⠀⠟⣯⡷⣞⣻⣽⢿⣯⣟⣯⣟ ⣯⡷⣞⣻⣷⣞⢷⣯⡷⣟⣯⠳⠙⠈⠁⠀⡀⣦⣴⢀⠁⠁⠊⠷⣯⣷⣞⣻⣷⣞⡷⢯⢷⣻⢷⣯ ⣽⣻⣿⣟⣯⣟⣻⣽⣿⡟⣻⣽⡿⣟⣻⢿⡟⣽⣻⠿⣟⣯⣟⣻⣽⣻⣿⣟⣯⣟⣻⣽⣿⡟⣻⣿

⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠒⠒⠒⠒⠁⠉⠁⠉⠁⠈⠉⠁⠉⠉⠉⠉⠉⠈ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⣀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠠⠄⠄⠄⠀⠠⠤⠄⡧⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖⠤⠤⠧⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰ ⠀⠀⠆⠒⠒⠒⠒⠒⠖⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀

⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠖⠒⠒⠒⠒⠒⠆⠀⠀ ⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠧⠤⠤⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡧⠄⠤⠠⠀⠄⠄⠄⠠⠤⠤⠠⠤⠤⠤⠤⠤⠤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆ ⠈⠉⠉⠉⠉⠉⠁⠉⠈⠁⠉⠁⠉⠁⠒⠒⠒⠒⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇